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Simplifying x2 + 20x + 40 = 0 Reorder the terms: 40 + 20x + x2 = 0 Solving 40 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 20x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 20x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 20x + x2 = 0 + -40 20x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 20x + x2 = -40 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -40 + 100 Reorder the terms: 100 + 20x + x2 = -40 + 100 Combine like terms: -40 + 100 = 60 100 + 20x + x2 = 60 Factor a perfect square on the left side: (x + 10)(x + 10) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 10) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 10 = 7.745966692 Simplifying x + 10 = 7.745966692 Reorder the terms: 10 + x = 7.745966692 Solving 10 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 7.745966692 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.745966692 + -10 x = 7.745966692 + -10 Combine like terms: 7.745966692 + -10 = -2.254033308 x = -2.254033308 Simplifying x = -2.254033308Subproblem 2
x + 10 = -7.745966692 Simplifying x + 10 = -7.745966692 Reorder the terms: 10 + x = -7.745966692 Solving 10 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -7.745966692 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.745966692 + -10 x = -7.745966692 + -10 Combine like terms: -7.745966692 + -10 = -17.745966692 x = -17.745966692 Simplifying x = -17.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.254033308, -17.745966692}
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